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*DECK ZACAI
SUBROUTINE ZACAI (ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL,
+ ELIM, ALIM)
C***BEGIN PROLOGUE ZACAI
C***SUBSIDIARY
C***PURPOSE Subsidiary to ZAIRY
C***LIBRARY SLATEC
C***TYPE ALL (CACAI-A, ZACAI-A)
C***AUTHOR Amos, D. E., (SNL)
C***DESCRIPTION
C
C ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA
C
C K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN)
C MP=PI*MR*CMPLX(0.0,1.0)
C
C TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT
C HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1.
C ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND
C RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON
C IS CALLED FROM ZAIRY.
C
C***SEE ALSO ZAIRY
C***ROUTINES CALLED D1MACH, ZABS, ZASYI, ZBKNU, ZMLRI, ZS1S2, ZSERI
C***REVISION HISTORY (YYMMDD)
C 830501 DATE WRITTEN
C 910415 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE ZACAI
C COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY
DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR,
* CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI,
* RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI, D1MACH, ZABS
INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ
DIMENSION YR(N), YI(N), CYR(2), CYI(2)
EXTERNAL ZABS
DATA PI / 3.14159265358979324D0 /
C***FIRST EXECUTABLE STATEMENT ZACAI
NZ = 0
ZNR = -ZR
ZNI = -ZI
AZ = ZABS(ZR,ZI)
NN = N
DFNU = FNU + (N-1)
IF (AZ.LE.2.0D0) GO TO 10
IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20
10 CONTINUE
C-----------------------------------------------------------------------
C POWER SERIES FOR THE I FUNCTION
C-----------------------------------------------------------------------
CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM)
GO TO 40
20 CONTINUE
IF (AZ.LT.RL) GO TO 30
C-----------------------------------------------------------------------
C ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION
C-----------------------------------------------------------------------
CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM,
* ALIM)
IF (NW.LT.0) GO TO 80
GO TO 40
30 CONTINUE
C-----------------------------------------------------------------------
C MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION
C-----------------------------------------------------------------------
CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL)
IF(NW.LT.0) GO TO 80
40 CONTINUE
C-----------------------------------------------------------------------
C ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION
C-----------------------------------------------------------------------
CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM)
IF (NW.NE.0) GO TO 80
FMR = MR
SGN = -DSIGN(PI,FMR)
CSGNR = 0.0D0
CSGNI = SGN
IF (KODE.EQ.1) GO TO 50
YY = -ZNI
CSGNR = -CSGNI*SIN(YY)
CSGNI = CSGNI*COS(YY)
50 CONTINUE
C-----------------------------------------------------------------------
C CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE
C WHEN FNU IS LARGE
C-----------------------------------------------------------------------
INU = FNU
ARG = (FNU-INU)*SGN
CSPNR = COS(ARG)
CSPNI = SIN(ARG)
IF (MOD(INU,2).EQ.0) GO TO 60
CSPNR = -CSPNR
CSPNI = -CSPNI
60 CONTINUE
C1R = CYR(1)
C1I = CYI(1)
C2R = YR(1)
C2I = YI(1)
IF (KODE.EQ.1) GO TO 70
IUF = 0
ASCLE = 1.0D+3*D1MACH(1)/TOL
CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF)
NZ = NZ + NW
70 CONTINUE
YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I
YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R
RETURN
80 CONTINUE
NZ = -1
IF(NW.EQ.(-2)) NZ=-2
RETURN
END
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